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  Rank jumps on elliptic surfaces and the Hilbert property

Loughran, D., & Salgado, C. (2022). Rank jumps on elliptic surfaces and the Hilbert property. Annales de l'Institut Fourier, 72(2), 617-638. doi:10.5802/aif.3457.

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Item Permalink: https://hdl.handle.net/21.11116/0000-000A-D1BB-7 Version Permalink: https://hdl.handle.net/21.11116/0000-000E-1D5E-A
Genre: Journal Article

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Loughran-Salgado_Rank jumps on elliptic surfaces and the Hilbert property_2022.pdf (Publisher version), 2MB
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Article mis à disposition par ses auteurs selon les termes de la licence Creative Commons attribution – pas de modification 3.0 France http://creativecommons.org/licenses/by-nd/3.0/fr/
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https://doi.org/10.5802/aif.3457 (Publisher version)
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https://doi.org/10.48550/arXiv.1907.01987 (Preprint)
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 Creators:
Loughran, Daniel, Author
Salgado, Cecília1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Number Theory, Algebraic Geometry
 Abstract: Given an elliptic surface over a number field, we study the collection of
fibres whose Mordell-Weil rank is greater than the generic rank. Under suitable
assumptions, we show that this collection is not thin. Our results apply to
quadratic twist families and del Pezzo surfaces of degree 1.

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Language(s): eng - English
 Dates: 2022
 Publication Status: Issued
 Pages: 22
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1907.01987
DOI: 10.5802/aif.3457
 Degree: -

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Title: Annales de l'Institut Fourier
Source Genre: Journal
 Creator(s):
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Publ. Info: Institut Fourier
Pages: - Volume / Issue: 72 (2) Sequence Number: - Start / End Page: 617 - 638 Identifier: -